Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.11, Problem 42E

**(a)**

To determine

**To express:** Kepler’s Third Law of planetary motion as equation.

Expert Solution

The equation of Kepler’s third law of planetary motion is

Kepler’s third law of planetary motion:

The square of the period

Direct variation:

If the quantities

Mathematically,

Here,

Thus Kepler’s third law as equation is

**(b)**

To determine

**To find:** The constant of proportionality

Expert Solution

The value of constant of proportionality is

**Given:**

Time period for our planet is

Average distance between sun and our planet is

**Calculation:**

Kepler’s Law as equation,

Substitute

Thus the value of constant of proportionality is

**(c)**

To determine

**To find:** The time period of Neptune.

Expert Solution

The time period of Neptune is

**Given:**

Distance of Neptune from Sun is

**Calculation:**

The value of constant of proportionality from part(b) is

Use Kepler’s third Law,

Substitute

Take square root of above equation and get the value of

Thus, time period of Neptune is approximately